Method and apparatus for predicting properties of a chemical mixture

ABSTRACT

The present invention relates to a method and apparatus for predicting the non-color properties of a chemical mixture, such as an automotive paint, using an artificial neural network. The neural network includes an input layer having nodes for receiving input data related to the chemical components of the mixture and environmental and process conditions that can affect the properties of the mixture. An output layer having nodes generate output data which predict the properties of the chemical mixture as a result of variation of the input data. A hidden layer having nodes is connected to the nodes in the input and output layers. Weighted connections connect the nodes of the input, hidden and output layers and threshold weights are applied to the hidden and output layer nodes. The connection and threshold weights have values to calculate the relationship between input data and output data. The data to the input layer and the data to the output layer are interrelated through the neural network&#39;s nonlinear relationship. When implemented, accurate predictions of the final properties of the mixture can be obtained. The invention is especially useful in relating automotive paint formulation variables (e.g., paint ingredient amounts and application process conditions) to physical properties (e.g., viscosity, sag), appearance (e.g., hiding, gloss, distinctness of image) or other measured properties enabling comparison of formula properties to target values or tolerances without expensive experimental work.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application is a continuation of U.S. patent applicationSer. No. 10/911,020, filed Aug. 3, 2004.

TECHNICAL FIELD

The invention relates to a method and an apparatus for predicting theproperties of a chemical mixture, such as a paint, with a high degree ofaccuracy, using artificial neural networks.

BACKGROUND OF THE INVENTION

Chemical mixtures, such as automotive paints, are commonly formulated toachieve desirable properties represented by property measurements. Agreat deal of effort, however, must be spent by laboratory personneldeveloping these formulas to provide the correct balance of properties.

For example, an automotive paint or coatings formulation consists of acomplex mixture of colorants (tints), binders and solvents formulated toprovide a balance of properties for color match, appearance, durability,application and film properties. Models are available for quantitativeprediction of the color of a mixture but not other properties. Hence,labor-intensive verification experiments are required to measure acoating formulation's properties to assure the values are withinacceptable limits.

Such experiments are needed because the relationships between themixture components and the measured properties are typically complex andunknown. In these cases it would be advantageous to develop predictivemodels that are capable of relating the mixture components to theproperties so that the properties of new mixtures can be estimated.While there have been various attempts to develop predictive models forchemical mixtures, none have gained widespread use in the art.

It would be desirable to provide a method and apparatus capable ofpredicting the non-color as well as color properties of chemicalmixtures, such as coating formulations, so as to enable an operator todetermine what input parameters are needed to obtain predeterminedproperties in the final coating.

Neural networks are one class of predictive models that have beenapplied to develop empirically-trained models relating processproperties to process variables, as shown in Piovoso, M. J. and A. J.Owens, 1991, Sensor data analysis using artificial neural networks, inArkun and Ray, eds., Chemical Process Control CPC-IV, AlChE, New York,101-118. Neural network methods are employed herein to developpredictive models of the properties of chemical mixtures.

SUMMARY OF THE INVENTION

A method and apparatus for predicting the measured properties of achemical mixture, such as a coating, are provided that employ artificialneural networks.

The method and apparatus are particularly useful for predicting thenon-color properties of automotive coatings formulations.

In one embodiment, the neural network includes an input layer havingnodes for receiving input data related to the coating formulation(component concentrations). Weighted connections connect the nodes ofthe input layer and have coefficients for weighting the input data. Anoutput layer having nodes are either directly or indirectly connected tothe weighted connections contained in hidden layers. The output layergenerates output data that is related to the non-color properties of thecoating. The data of the input layer (component concentrations) and thedata from the output layer (measured properties) are interrelatedthrough the neural network's nonlinear relationship and can be used,once the neural network is trained, to predict the measured propertiesof a coating formulation.

Empirical data consisting of historical chemical mixture data and themeasured properties of the mixtures is used to train the network weightsusing a backpropagation method of supervised training. The trainednetwork is then used to predict the measured properties of new chemicalmixtures by a feed forward calculation. The invention is useful indescribing the relationship between chemical mixture variables and themeasured properties of the mixture. The trained network can predict theproperties of new chemical mixtures without costly experimentalverification.

The chemical mixture neural network can be used for, but not limited to,predicting properties of new mixtures, identifying formula mistakes, orfor formula corrections.

Additional advantages and aspects of the present invention will becomeapparent from the subsequent description and the appended claims, takenin conjunction with the accompanying drawings in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a generalized diagram depicting the structure of the presentinvention's chemical mixture neural network;

FIG. 2 is a generalized diagram illustrating the calculation process atone node of a chemical mixture network; and

FIG. 3 is a block diagram illustrating the network training and forwardprediction processes.

DETAILED DESCRIPTION OF THE INVENTION

The invention provides a method and apparatus for predicting theproperties of a chemical mixture. The invention employs acomputer-implemented artificial neural network. The neural networkcontains at least two layers of processing elements, an input and outputlayer. The processing elements are interconnected in a predeterminedpattern with predetermined connection weights therebetween. The networkhas been previously trained to simulate the response of the chemicalmixture to variation of inputs thereto. When trained, the connectionweights between the processing elements contain information regardingthe relationship between the components of a chemical mixture (inputs)and the measured properties (outputs) of the mixture, which can be usedto predict the final properties of the chemical mixture to variation inthe mixture components.

Since the method of the invention is based on historical data offormulation and property values, the prediction of property values usingsuch method typically have an error approaching the error of theempirical data, so that the invention predictions are often just asaccurate as verification experiments.

Referring now to the drawings, FIG. 1 shows a chemical mixture neuralnetwork generally depicted at 10. The chemical mixture neural network 10is configured as a backpropagation network which includes threeprocessing layers (or three neuron layers), an input layer 12, a hiddenlayer 14, and an output layer 16. The network is organized such that theinput layer 12 contains a set of at least one to i processing elementscalled input nodes, the hidden layer 14 has a set of at least one to jprocessing elements called hidden nodes, and the output layer 16 has aset of at least one to k processing elements called output nodes. Theprocessing elements or nodes are interconnected such that therelationship between chemical mixture component and process conditioninputs and measurement property outputs can be simply calculated, whenthe network is implemented.

In the present invention as shown in FIG. 1, the processing network isorganized such that the input layer 12 contains one node (In) for eachchemical mixture or process input variable of the model. The input nodesare fully connected to hidden nodes (H) of the hidden layer 14 of thenetwork and the hidden nodes are fully connected to the output nodes(Out) of an output layer 16 of the network. There is one input node foreach mixture component or process condition input variable and oneoutput node for each process property measurement output. The connectionline arrows (L) indicate the direction of the calculation from inputvalues through the network to the output values. The number of hiddennodes can be varied with increasing number of hidden nodes adding to thenetwork capability to model complexity of the input to outputrelationship. Each connection line has a connection weight associatedwith it and each hidden and output node has one additional thresholdweight. The network weights are the parameters of the network that allowthe network to model the input to output relationship. Networks withmultiple hidden layers and networks that are not fully connected arepossible alternative network structures but the fully connectedthree-layer network is sufficient for modeling chemical mixtureprocesses.

FIG. 2 is a generalized representation of the calculation process shownat one node 18, but which is used throughout the network. The nodes arethe processing or calculating elements of the network. Each node 18refers to the calculation process at hidden and output nodes. Each node18 has an input port P_(in) and an output port P_(out). The node isresponsive to one or a plurality of excitation or intensity signal(s) I₁through I_(m) presented at the input port P_(in) and is operative toproduce an activation signal Q_(out) carried on a line L_(out) connectedat the output port P_(out). Each of the input intensity values I₁through I_(m) is connected to the input port P_(in) of the node 18 overa respective line L₁ through L_(m) that has a predetermined respectiveconnection weight W₁ through W_(m). A threshold weight (T) without anyinput connection provides a threshold level for the node input. This isequivalent to one additional input connection line L_(m+1) to the nodewith a constant excitation signal or intensity I_(m+1) of 1. Theactivation signal Q_(out) that is produced on line L_(out) at the outputport P_(out) of the node is a function of the input signal Q_(in)applied at the input port P_(in). The input signal Q_(in) is thesummation, over all of the input lines to the node, of the product ofthe intensity of a given excitation signal I and the connection weight Wof the line L carrying the signal to the node plus the threshold weightas shown in Equation 1. $\begin{matrix}{Q_{in} = {T + {\sum\limits_{z = 1}^{m}{w_{z}I_{z}}}}} & (1)\end{matrix}$

The node output (Q_(out)) is computed by a non-linear squashing function(S) that limits Q_(out) to a finite range for any value of Q_(in). Thetypical squashing function is the logistic function as shown in equation2 but any non-linear monotonic increasing function could be used.S=(1+exp(−Q _(in)))⁻¹  (2)

The node output then is the squashed non-linear response to the linearnode inputs as shown in equation 3 and as carried on one or more lines(L_(out)) to nodes in the next network layer.Q _(out) =S(Q _(in))  (3)

The node outputs are then the intensities of the inputs to the nodes inthe next layer of the network. The node calculation is carried out atall hidden and output layer nodes but not at input layer nodes. Theinput layer has a single input intensity value and no squashingfunction. The input layer nodes simply represent the input dataintensity values. The Q_(out) values of the output layer are the networkestimates of the property values.

It is usual to scale all input and output values of the network to aconvenient range such as 0 to 1. The unscaled input and output datavalues are transformed to fall within this range. The transformation canbe any monotonic function with output in the range 0 to 1. Typically thescaling operation is a linear transform but logarithmic, exponential orother monotonic transforms of a single variable can also be used.

The usual practice is to use the same scaling operation for inputs oroutputs with common data characteristics. For example all mixturecomponents have intensities between 0 and 1 and thus all can use thesame input scaling transform. Conversely input or output values withdissimilar number scales (e.g. mixture components (0 to 1), processtemperature (60 F to 90 F)) will typically have different scalingtransformations.

To build such a neural network that can be used to predict theproperties of a chemical mixture, the method of the invention comprisesfour phases: data collection, network structure, training and forwardprediction.

Data collection provides empirical information to train the network.Chemical mixture component amounts and mixture property measurements areobtained from process history or calibration experiments. Additionalprocess variables such as environmental conditions or chemical mixtureapplication conditions may influence the measured property values. Datafor these independent variables are collected for use in modeling therelationships between process inputs and outputs.

A network structure is constructed with input nodes for each processvariable (mixture components and process conditions), one or more hiddennodes and outputs nodes for each process property measurement. The nodesare fully connected by weight connections between input and hidden andbetween hidden and output nodes. Additional threshold weights areapplied to the hidden and output nodes. Each network node represents asimple calculation of the weighted sum of inputs from prior nodes and anon-linear output function. The combined calculation of the networknodes relates the process inputs to the outputs. Separate networks canbe developed for each property measurement or groups of properties canbe included in a single network.

Training estimates network weights that allow the network to calculateoutput values close to the measured output values. A supervised trainingmethod is used in which the process output data is used to direct thetraining of the network weights. The network weights are initializedwith small random values or with the weights of a prior partiallytrained network. The process data inputs are applied to the network andthe output values are calculated for each training sample. The networkoutput values are compared to the measured output values. Abackpropagation algorithm is applied to correct the weight values indirections that reduce the error between measured and calculatedoutputs. The specific type of backpropagation algorithm used is a stiffordinary-differential-equation algorithm as described in U.S. Pat. No.5,046,020 issued to David L. Filkin, Distributed Parallel ProcessingNetwork Wherein the Connection Weights are Generated Using StiffDifferential Equations, and in Owens, A. J. and D. L. Filkin, 1989,Efficient training of the back propagation network by solving a systemof stiff ordinary differential equations, International Joint Conferenceon Neural Networks, Washington, D.C., 2, 381-386, which disclosures arehereby incorporated by reference. The process is iterated until nofurther reduction in error can be made. A cross-validation method isemployed to split the data into training and testing data sets. Thetraining data set is used in the backpropagation training of the networkweights. The testing data set is used to verify that the trained networkgeneralizes to make good predictions on independent chemical mixtures.The best network weight set is taken as the one that best predicts theoutputs of the test data set. Similarly varying the number of networkhidden nodes and determining the network that performs best with thetest data optimizes the number of hidden nodes.

Forward prediction uses the trained network to calculate estimates ofprocess outputs for new chemical mixtures. A new set of mixture andprocess values is input to the trained network. A feed forwardcalculation through the network is made to predict the output propertyvalues. The predicted measurements can be compared to property targetvalues or tolerances. If the predicted property values are unacceptable,varying the process-input values can make a correction.

When implementing the network, the mixture components and optionallyprocess conditions are considered the inputs to the chemical mixturemodel and the measured properties are considered the outputs of thechemical mixture model. Variation in the measured properties is relatedto variation in the mixture components. That is the mixture componentsare the independent variables of the process and the measured propertiesare dependent variables of the process.

Mixture components are expressed as fractional concentrations of thetotal amount of the mixture. In general the property of a mixturedepends on the component fractional concentrations rather than the totalamount of the mixture. For example a 50:50 volume mixture of water andantifreeze has a freezing temperature of −30 F and the freezingtemperature does not depend on whether the mixture sample amount is 1 mlor 1 l. Mixture formulas can be expressed in weight, volume or otherquantity units. The fractional concentration is simply the quantity of acomponent in the mixture divided by the total quantity of the mixture.The sum of the fractional concentrations will be unity. Fractionalconcentrations are continuous variables in the range 0 to 1.

Properties of the mixture can be any measurable characteristic. Thecharacteristic can be a continuous, ordinal or nominal measurement. Forexample a formulated coating could have a measurement of the viscosityof the liquid mixture on a continuous scale. Another measurement couldbe the measurement of orange peel of the applied coating film on a 10category ordinal scale from 1 (very unsmooth) to 10 (very smooth). Anexample of a nominal measurement could be the coded categories of passor fail for observation of some defect.

Many times the measured properties of mixtures depend on processvariables in addition to the mixture components. For exampleenvironmental variables may influence a property measurement. In thecoating example above the temperature of the mixture during measurementcan influence the measurement of viscosity. Inclusion of temperature asa process input variable could improve the model performance.Application variables can also influence the property measurements andcan be included in the process model as inputs. A mixture might beprocessed on equipment A, B or C. Three binary variables could be usedto code for the equipment nominal variable as shown in table 1. TABLE 1Example of the use of binary variables to code for three levels of anominal variable Variable Equipment A Equipment B Equipment C X1 1 0 0X2 0 1 0 X3 0 0 1

Thus the process model has one continuous input for each chemicalmixture component and optionally can have additional continuous, ordinalor nominal non-mixture process inputs. In a similar fashion the processmodel can have one or more measured outputs and the outputs can becontinuous, ordinal or nominal variables.

A single example of a set of process input and output values is calledan exemplar. A collection of input and output data values is required todevelop the process model. These exemplars can be obtained from either aprocess calibration experiment or process history.

The process data should cover the useful range of each of the processinputs. For example if mixture component A is used in the range 0 to 0.1and component B in the range 0.3 to 0.7 then the process data shouldinclude samples with several levels of A and B within these constrainedranges. Since the input to output relationship is frequently complex,non-linear and interactive the samples should cover the useful range incombinations with multiple levels of other process inputs. A calibrationexperiment is designed to sample the mixture design space and includevarying levels of the mixture components. Some of these samples may bepure mixtures or simple binary or ternary blends. It is useful to alsoinclude complex mixtures that simulate the usual multi-componentmixtures of the process.

Alternatively process history data can be collected from the routineoperation of the process. Sometimes the routine process may not samplethe full potential range of a process variable or there may be fewexemplars for a particular mixture component. Combination of processhistory and calibration data can overcome this problem. The calibrationdata assures that each component is adequately sampled over its designrange while the history data provides samples in frequently used regionsof the mixture space.

The process data is used to train the chemical mixture network.Cross-validation splits the process data into training and testing datasets. Typically 80% of the data is used to train the network and 20% isreserved for estimating the error of the network with data that isindependent of the training. The testing data set allows the networkdeveloper to verify that the trained network relationship betweenprocess inputs and outputs will generalize to new exemplars.

When the network is trained, it provides a model of the relationshipbetween chemical mixture component and process condition inputs andmeasurement property outputs. When implemented, as shown in FIGS. 1 and2, the network can simply calculate measured properties based onvariation of inputs to a high degree of accuracy.

FIG. 3 is a block diagram depicting the process for supervised trainingof the chemical mixture neural network. Training exemplars areintroduced to the input block (I) and fed forward to the network block(N) that computes the output estimates in the output block (O). Errorblock (E) contains the observed differences between the output estimates(O) and the measured property values (M). Supervised training refers tothe use of known output measurement values to guide the training of thenetwork weights to minimize the differences between the output estimatesand the output measurements. Training uses a backpropagation trainingalgorithm. A network structure with one or more hidden nodes is assumed.The network weights are initialized by one of two methods. In the firstmethod all of the network weights are given small random values. In asecond method a prior trained network with h hidden nodes is used toinitialize a network with more than h hidden weights. The connection andthreshold weights associated with the added hidden nodes are initializedwith small random values and the remaining weights are initialized byadopting the weights of the prior network. Each training exemplar isapplied to the network and the output estimates and differences areobtained. The backpropagation algorithm (B) adjusts the network weightsin small steps in directions that reduce the differences. Thebackpropagation algorithm iterates until a local minimum of the leastsquared error of the differences is obtained. The rms (root mean square)error of the differences is found and represents the estimated error ofthe network for the training exemplars.

The trained network is verified by cross-validation. The test exemplarsare input to the network obtaining output estimates that are compared tothe known output values to determine differences. The rms error of thetest data set is compared to the rms error of the training data set. Thebest of a set of models at varying number of training iterations istaken as the network with minimum test error. This is the network thatbest generalizes the input to output relationship to new independentexemplars. Similarly, networks at varying number of hidden units arecompared and the network with minimum test rms error is taken as thebest network.

The trained chemical mixture network is then employed to makepredictions of the property measurements of new exemplars by forwardprediction. New sets of input values are introduced to the network (I),fed forward through the network calculation (N) to predict estimates ofthe property values (O). Estimated property values can be compared totarget values or tolerance limits to determine whether the mixture issuitable for its intended purpose. The sensitivity of the outputestimates to variation of the input values in the vicinity of the inputmixture can be determined and used to guide interactive or automatedadjustment of the input values to yield acceptable property estimates.

The following examples are given to illustrate the invention and shouldnot be interpreted as limiting in any way.

In particular, these examples illustrate the invention in the context ofpredicting the non-color properties of automotive coating formulations,for example, physical properties (viscosity, sag) and appearance(hiding, gloss, distinctness of image) when input variables (paintingredient amounts, application process conditions) are varied. Oneskilled in the art would understand that the method of the presentinvention also is useful for predicting the properties of other kinds ofchemical mixtures, whether solids or liquids, including, but not limitedto, other types of paints and coatings, inks including ink jet inks,alcohols, diesel fuel, oil, plastics, polymer blends, films, and thelike.

EXAMPLE 1

Neural networks were developed to predict the relationship betweencoatings formulations and substrate hiding in automotive collisionrepair coatings systems. Four collision repair coatings systems coded A,B, C, D were used. All four systems are intermix systems of singlepigment tint and binder components that can be combined to make a widevariety of colors to match an automotive color being repaired. Systems Aand C are used for repair of solid automotive colors and systems B and Dare used to repair automotive colors containing metallic or pearlescentflakes. We denote the latter type of colors as effect colors. Thecoating mixture to be used for a repair is defined by a formulaindicating the mass amounts of the components to make a customary volumeof the liquid coating. For example the formula component amounts ingrams to make a gallon volume could be used. The property to bepredicted is the film thickness required to eliminate the visualcontrast of the color over black and white substrates. We call thisproperty black and white hiding and measure the property by a methoddescribed under Test Methods. Hiding is measured as a film thickness andin our case we measure thickness in mil units.

Process formula and hiding data were obtained for the four coatingssystems. For systems A and B new calibration samples were preparedincluding ladders of each tint in blends with either a white tint forsolid colors or an aluminum flake tint for effect colors. In additionhistorical process formulas were prepared with new measurements ofhiding. Some formulas were made at two levels of the ratio of pigmentsolid mass to binder solid mass (called the pigment to binder ratio,P/B) to provide variation in the binder level for similar colorformulas. For systems C and D the formulas and hiding data were takenfrom historical process records.

The tint and binder component formulas were normalized so that thecomponent mass concentrations sum to 1. All component concentrationsused a common linear scaling to provide the inputs to the network.Measured hiding was logarithmically scaled to form the output of thenetwork. Network hiding estimates are transformed to the natural unitsfor comparison to the measured hiding values.

Networks were trained by backpropagation at varying number of hiddenunits and the best network determined by the cross-validation method.Table 2 summarizes the results for the chemical mixture predictionnetworks for the four coatings systems. The network structure (I-H-O)gives the number of nodes in the input, hidden and output layers of thenetwork. The process hiding data is summarized by count, data mean, dataminimum and data maximum. The network prediction performance is shown bythe standard deviation of the residuals between the estimated andmeasured hiding values. TABLE 2 Summary of chemical mixture predictionnetworks for four coatings systems Residual Data Data Data standardNetwork Data Mean Min Max deviation System (I-H-O) count (mil) (mil)(mil) (mil) A 43-3-1 527 1.32 0.14 7.21 0.21 B 64-2-1 723 0.79 0.11 8.270.24 C 41-2-1 1925 1.24 0.08 6.00 0.28 D 69-3-1 11232 0.65 0.12 5.200.14

Multiple linear regression (MLR) models were developed for hiding as afunction of a mixture model of the components for coatings systems A andB. The residual standard deviations for the network and MLR models were0.21 and 0.49 respectively for system A and 0.24 and 0.32 respectivelyfor coatings system B. In both cases the chemical mixture predictionnetwork has lower residual error than a MLR model with the same mixturecomponent inputs.

Coatings mixture networks for hiding prediction for systems A, B, C, andD are implemented in proprietary software for automotive color matchingto aid the technician in adjusting binder level to meet process goalsfor hiding. The software provides a hiding estimate by forwardprediction for any mixture of the coatings system components.

EXAMPLE 2

A collection of about 3300 solid colors was developed in a coatingsintermix system for the heavy-duty truck fleet market. There was desireto provide property estimates for the color formulas in this specialcollection. The properties of interest included black and white hiding,viscosity, appearance, orange peel and sag. Measurements of theseproperties are described under Test Methods.

The formulas and property measurement data were taken from the first1213 color formula developments. These data include a small number ofcalibration samples at or near the masstone formula for single tintswith appropriate balancing binder additions. The remainder were actualprocess formulas. Property measurements for 100 color formulas wererepeated to estimate the replication error of the property measurements.At the time the data was extracted some of the property data wasincomplete so that between 1088 and 1200 exemplars were available forthe various property measurements.

Fourteen single pigment tints and one binder were the components of themixtures. The weight formulas were normalized so that the sum of thecomponents was 1 and the components are in fractional mass concentrationunits. The appearance network had an additional process variable forcoating film thickness in mil. The mixture components all used the samelinear input transform. The film thickness input had a separate linearinput transform.

Correlated property measurements were grouped within a network. Forexample, a viscosity prediction network had outputs for unactivatedviscosity, activated viscosity at time 0 min., activated viscosity at 30min. and activated viscosity at 60 min. In another example an appearancenetwork had outputs for 20-degree gloss, 60-degree gloss anddistinctness of image. The remaining properties of hiding, orange peeland sag each had a separate network. All outputs were linearly scaled.

Chemical mixture prediction networks were trained by backpropagation foreach set of properties at varying number of hidden units with the bestnetwork selected by the cross-validation method. Table 3 summarizes theresults. The residual standard deviation between network propertyestimates and measurements is comparable to the standard deviation ofdifferences between replicate property measurements. The networkpredictions are as accurate as property measurements. TABLE 3 Summary ofchemical mixture prediction networks for an intermix coatings systemResidual Replicate Network Data Data standard standard Property SetProperties (I-H-O) count Mean Data Min Data Max deviation deviationHiding 15-3-1 1103 1.01 0.4 5.5 0.19 0.20 Viscosity unactivated 15-4-41088 11.2 8.2 27.1 0.90 0.75 activated 0 10.5 7.9 16 0.68 0.72 activated30 11.9 8.7 17.5 0.82 0.89 activated 60 13.5 9.9 20.1 1.08 1.12Appearance 20 gloss 16-4-3 1101 88.7 44 95 3.33 3.63 60 gloss 95 83 991.25 1.86 DOI 81.7 15 96 7.55 11.43 Orange peel 15-4-1 1103 6.6 2 8 0.580.80 Sag 15-2-1 1200 2.9 1.6 9.2 0.51 0.49

Forward prediction using the chemical mixture property predictionnetworks was employed to estimate the properties of 2200 additionalcolor formulas in the special solid color collection.

TEST METHODS USED IN THE EXAMPLES

The following test methods were used for generating data reported in theexamples above:

Hiding Measurement

Visual black and white hiding of an automotive coating is measured bydetermining the visual threshold for contrast of the coating over blackand white substrates. A black and white contrast test strip (Lenetablack & white spray monitors, form M71 or equivalent) is adhered to a4×12 inch aluminum or steel substrate panel. The coating is sprayapplied to the panel with film thickness variation in a continuousgradient from thin at one end of the panel to thick at the other end sothat the hiding contrast threshold appears in the center third of thepanel. For example, if the hiding contrast threshold occurs at 1.5 milthen the wedge is prepared so that the film thickness varies from about1 mil at the thin end to about 2 mil at the thick end. The test sampleis called a hiding wedge. The hiding wedge is viewed by a technicianunder standardized lighting conditions. The technician determines theposition on the hiding wedge where the visual contrast between thecoating color over black and over white just disappears. This is thevisual hiding contrast threshold. The thickness of the coating over thesteel or aluminum substrates at the threshold position is measured andreported as the black and white hiding value. Hiding values are usuallyreported in mil or micrometer units.

Sag Measurement

Sag for an automotive coating is the film thickness at which avertically applied coating appears to sag or drip down the verticalsurface. The test coating is vertically applied with varying filmthickness along one dimension of a sag test panel. The sag test panel isa 10 by 10 inch steel substrate with electrocoat primer and with sixmetal rivet heads spaced along the upper region of the panel. Sag ismarked in the area below rivet heads where a teardrop forms or where a ½inch windowpane is measured at the top of the panel (whichever occurs1^(st)). The sag sample is spray applied with the rivets in a verticalposition on the left or right side of the panel and is baked verticallywith the rivets aligned horizontally at the top of the panel accordingto the product specification. The technician visually observes the sagtest sample and determines the position where sag first occurs. Thecoating film thickness is measured at the sag position and the sag valueis reported as a film thickness in mils or micrometers.

Viscosity Measurement

The viscosity of a liquid paint sample is determined by measuring thetime required for a known volume of the paint to flow through a hole ofknown diameter in a viscosity cup. The method is equivalent toASTM-D-1084, Method D. A Zahn viscosity cup supplied by Paul N. Gardner,Pompano Beach, Fla. 33060 or equivalent is used. The cup consists of a44+−0.5 ml stainless steel cup with wire handles and a fixed diameterefflux hole. The paint sample fills the fixed volume of the cup. Astopwatch or other timing device is employed to measure the time elapsedbetween the start of efflux and the first break in the stream exitingthe efflux hole. Viscosity is reported in seconds of efflux.

In reactive two-component paint systems it is useful to monitor theincrease in viscosity after the paint is activated with a reactioninitiator. The viscosity of the unactivated paint, activated paintimmediately after activation, activated paint after 30 minutes andactivated paint after 60 minutes are measured to assure that viscosityremains within acceptable ranges.

Appearance Measurements

A coating sample is applied and baked according to the productspecification to prepare a test sample for appearance measurements.Orange peel is determined by visual comparison of the test samplesurface texture to a series of orange peel standards varying in 10 stepsfrom very rough texture (scale 1) to very smooth texture (scale 10). Theorange peel reference standards are supplied by ACT Laboratories Inc.,Hillsdale, M149242 as product Apr14941 at. Gloss is measured by aprocess equivalent to ASTM D523-89 Standard Test Method for SpecularGloss. A HunterLab ProGloss PG-3 gloss meter or equivalent measures thetest sample gloss at 20 and 60 degree angles of specular reflection.Distinctness of image is measured by a process equivalent to ASTME430-97 Standard Test Method for Measurement of Gloss of High-GlossSurfaces by Goniophotometry using a HunterLab Dorigon II distinctness ofimage meter.

Various modifications, alterations, additions or substitutions of themethods and apparatus of this invention will be apparent to thoseskilled in the art without departing from the spirit and scope of thisinvention. This invention is not limited by the illustrative embodimentsset forth herein, but rather is defined by the following claims.

1. A method for predicting non-color properties of a coatingformulation, comprising: a) collecting history and/or calibration datamade up of coating formulation variables including coating formulationingredient amounts and optionally other environmental and applicationprocess variables and the corresponding measured properties of thesemixtures; b) developing a neural network having the capability ofassociating the contribution of the coating formulation variables to themeasured properties of the mixtures; c) supervised training of theneural network using history and/or calibration data so that the networkpredicts the relationship between the coating formulation variables andthe measured properties; d) employing the neural network to make forwardpredictions of gloss, distinctness of image, orange peel, viscosity, orsag measurements of said coating formulations.
 2. The method accordingto claim 1, wherein after step (d) the predicted non-color propertiescan be compared to property performance targets, so that coatingformulation adjustments can be made to meet property performancetargets.
 3. The method of according to claim 1, wherein the neuralnetwork includes an input layer having a plurality of input nodes thatare associated with each mixture ingredient, environmental andapplication process variable, at least one hidden layer having hiddennodes, an output layer having one or more output nodes representingoutput properties of the mixture, weighted connections between the inputnodes of the input layer, the hidden nodes of the hidden layers and theoutput nodes of the output layer, and threshold weights on all hiddenand output nodes, wherein the weighted connections and threshold weightsdetermine the contribution of the mixture ingredients and optionally theother environmental and process variables to the measured properties. 4.The method according to claim 1, wherein the historical and/orcalibration data further includes either or both environmental variablesand application process variables.
 5. The method according to claim 1wherein the measured non-color properties of the coating formulationinclude properties of the wet coating and/or properties of coatingsformed therefrom.
 6. A system for carrying out the method of claim 1,said system comprising: a) an input device for entering a coatingformulation recipe that contains two or more ingredients; b) a neuralnetwork previously trained to predict the measured property response ofthe coating formulation to variation in mixture ingredient amounts andoptionally environmental and process variables; c) an output device thatdisplays the predicted gloss, distinctness of image, orange peel,viscosity, or sag properties of the coating formulation entered into thenetwork using the input.
 7. The system according to claim 6, whereinafter the output device displays the predicted non-color properties, thepredicted properties can be compared to property performance targets, sothat coating formulation adjustments can be made to meet propertyperformance targets.
 8. The system according to claim 6, wherein theneural network includes an input layer having a plurality of input nodesthat are associated with each mixture ingredient, environmental andapplication process variable, at least one hidden layer having hiddennodes, an output layer having one or more output nodes representingoutput non-color properties of the mixture, weighted connections betweenthe input nodes of the input layer, the hidden nodes of the hiddenlayers and the output nodes of the output layer, and threshold weightson all hidden and output nodes, wherein the weighted connections andthreshold weights determine the contribution of the mixture ingredientsto the measured non-color properties.
 9. The system according to claim6, wherein the neural network is trained to predict the measuredproperty response of the coating formulation to variation in mixtureingredient amounts and either or both environmental and applicationprocess variables.
 10. A method for predicting a non-color property of acoating formulation, comprising: a) collecting history and/orcalibration data made up of coating formulation variables includingcoating formulation ingredient amounts and optionally otherenvironmental and application process variables and the correspondingmeasured properties of these mixtures; b) developing a neural networkhaving the capability of associating the contribution of the coatingformulation variables to the measured properties of the mixtures; c)supervised training of the neural network using history and/orcalibration data so that the network predicts the relationship betweenthe coating formulation variables and the measured properties; d)employing the neural network to make a forward prediction of theproperty of hiding of said coating formulation.
 11. A system forcarrying out the method of claim 10, said system comprising: a) an inputdevice for entering a coating formulation recipe that contains two ormore ingredients; b) a neural network previously trained to predict themeasured property response of the coating formulation to variation inmixture ingredient amounts and optionally environmental and processvariables; c) an output device that displays predicted hiding propertyof the coating formulation entered into the network using the input.